$$ \begin{aligned} 6x+27 &= 8\cdot\frac{1}{2}x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot6x+2\cdot27 &= 28\cdot\frac{1}{2}x&& \text{cancel out the denominators} \\[1 em]12x+54 &= 8x&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 54 }$ to the right} \\[1 em]12x-8x &= -54&& \text{simplify left side} \\[1 em]4x &= -54&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{54}{4}&& \\[1 em]x &= -\frac{27}{2}&& \\[1 em] \end{aligned} $$

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